# Binomial Theorem

## Exercises in expanding powers of binomial expressions and finding specific coefficients.

##### BracketsPascal's TriangleLevel 1Level 2Exam-StyleDescriptionHelpMore Algebra

This is level 2: finding specific coefficients

 1. If you expand the binomial expression $$(a + b)^5$$ the result would be:$${5 \choose 0} a^5 + {5 \choose 1} a^4 b + {5 \choose 2} a^3 b^2 + {5 \choose 3} a^2 b^3 + {5 \choose 4} ab^4 + {5 \choose 5} b^5$$Find the coefficient of the $$a^3 b^2$$ term 2. In the expansion of $$(c + d)^7$$ what is the coefficient of the $$c^3 d^4$$ term? 3. In the expansion of $$(e - f)^9$$ what is the coefficient of the $$e^2 f^7$$ term? 4. In the expansion of $$(2x + 3y)^4$$ what is the coefficient of the $$x^4$$ term? 5. In the expansion of $$(3x - 4y)^5$$ what is the coefficient of the $$y^5$$ term? 6. In the expansion of $$(2x + 3y)^4$$ what is the coefficient of the $$x^2y^2$$ term? 7. In the expansion of $$(3x - 4y)^5$$ what is the coefficient of the $$x^2y^3$$ term? 8. Find the the coefficient of the $$x^2$$ term in the expansion of $$(x^2 + \frac{1}{x} )^7$$ 9. Find the constant term in the expansion of $$(2x^2 - \frac{1}{2x} )^6$$ 10. Use the expansion of $$(5 + x)^3$$ to find the exact value of $$5.1^3$$.
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This is Binomial Theorem level 2. You can also try:
Level 1

## Instructions

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#### Four Colour Theorem

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

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## Description of Levels

Brackets - The basics of expanding brackets

Pascal's Triangle - See how the coefficients are generated

Level 1 - Complete expansions of binomials

Level 2 - Finding specific coefficients

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

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## Using a Scientific Calculator

The function to work out a number in Pascal's Triangle appears as nCr where:

## Using a Graphic Display Calculator

With a GDC you can work out a whole row of Pascal's Triangle using the combinations function. Here is a screenshot of the TI Nspire.

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### Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

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